I may give that a shot..would have to find a company that accepts prepaid cards. The last time I registered a domain with Godaddy, they required a photocopy of my driver's license, along with billing info.
I've never had to register another domain name since then, so haven't done it through any other companies, although I've used other hosts
I'll probably give that namecheap site a shot, using a prepaid card/fake info and see if they accept it